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User: Andi Fugard

Andi Fugard has authored 2 sequences.

A358693 Numbers k such that k / (sum of digits of k) is the square of a prime.

12, 24, 36, 48, 81, 150, 225, 375, 441, 735, 882, 1014, 1452, 1521, 1815, 2023, 2028, 2178, 2312, 2535, 2601, 3549, 3610, 4046, 4332, 4335, 4624, 4913, 5054, 5415, 5491, 5780, 6069, 6137, 6358, 6647, 6936, 7581, 7942, 8664, 8959, 9386, 9522, 9747, 10092, 11532, 12321, 12615, 12696

Offset: 1

Andi Fugard, Jan 01 2023

Terms k from A001102 such that k / (sum of digits of k) is the square of a prime.

Cf. A001102, A001248, A007953.

Select[Range[13000], PrimeQ[Sqrt[#/Plus @@ IntegerDigits[#]]] &] (* Amiram Eldar, Jan 01 2023 *)

isok(k) = my(r); issquare(k/sumdigits(k), &r) && (denominator(r)==1) && isprime(r); \\ Michel Marcus, Jan 01 2023

More terms from Michel Marcus, Jan 01 2023

A140961 Number of 3 X n {0,1}-matrices such that: (a) first and second row have a common 1, (b) second and third row have a common 1.

Original entry on oeis.org

1, 17, 205, 2129, 20341, 184457, 1615405, 13808609, 116015461, 962575097, 7913168605, 64610052689, 524855128981, 4247421698537, 34274519697805, 275985344786369, 2218709434248901, 17815093293410777, 142915542082163005, 1145704555158361649, 9179974972732223221

Offset: 1

Andi Fugard, Vladeta Jovovic, Jul 26 2008

Andi Fugard, Counting first-order models (with n individuals) of syllogisms.
Index entries for linear recurrences with constant coefficients, signature (19,-118,240).

Cf. A051588.

a(n) = 8^n-2*6^n+5^n.

G.f.: x*(2*x-1)/((5*x-1)*(6*x-1)*(8*x-1)). [Colin Barker, Nov 05 2012]

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User: Andi Fugard

A358693 Numbers k such that k / (sum of digits of k) is the square of a prime.

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A140961 Number of 3 X n {0,1}-matrices such that: (a) first and second row have a common 1, (b) second and third row have a common 1.

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